1 Overview

In this homework assignment, you will explore, analyze and model a data set containing approximately 2200 records. Each record represents a professional baseball team from the years 1871 to 2006 inclusive. Each record has the performance of the team for the given year, with all of the statistics adjusted to match the performance of a 162 game season.

We have been given a dataset with 2276 records summarizing a major league baseball team’s season. The records span 1871 to 2006 inclusive. All statistics have been adjusted to match the performance of a 162 game season.

Your objective is to build a multiple linear regression model on the training data to predict the number of wins for the team. You can only use the variables given to you (or variables that you derive from the variables provided).

Glossary of data

data.frame(
  `Variable Name` = c("INDEX","TARGET_WINS","TEAM_BATTING_H","TEAM_BATTING_2B","TEAM_BATTING_3B","TEAM_BATTING_HR","TEAM_BATTING_BB","TEAM_BATTING_HBP",
                      "TEAM_BATTING_SO","TEAM_BASERUN_SB","TEAM_BASERUN_CS","TEAM_FIELDING_E","TEAM_FIELDING_DP","TEAM_PITCHING_BB","TEAM_PITCHING_H","TEAM_PITCHING_HR","TEAM_PITCHING_SO"),
  `Definition` = c("Identification Variable (do not use)","Number of wins","Base Hits by batters (1B,2B,3B,HR)","Doubles by batters (2B)","Triples by batters (3B)","Homeruns by batters (4B)","Walks by batters","Batters hit by pitch (get a free base)","Strikeouts by batters","Stolen bases","Caught stealing","Errors","Double Plays","Walks allowed","Hits allowed","Homeruns allowed","Strikeouts by pitchers"),
  `THEORETICAL EFFECT` = c("None","","Positive Impact on Wins","Positive Impact on Wins","Positive Impact on Wins","Positive Impact on Wins","Positive Impact on Wins","Positive Impact on Wins","Negative Impact on Wins","Positive Impact on Wins","Negative Impact on Wins","Negative Impact on Wins","Positive Impact on Wins","Negative Impact on Wins","Negative Impact on Wins","Negative Impact on Wins","Positive Impact on Wins")
) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"),full_width = F)

Below is a short description of the variables of interest in the data set:

2 Deliverables

• A write-up submitted in PDF format. Your write-up should have four sections. Each one is described below. You may assume you are addressing me as a fellow data scientist, so do not need to shy away from technical details.
• Assigned predictions (the number of wins for the team) for the evaluation data set.
• Include your R statistical programming code in an Appendix.

3 DATA EXPLORATION

The data set describes baseball team statistics for the years 1871 to 2006 inclusive. Each record in the data set represents the performance of the team for the given year adjusted to the current length of the season - 162 games. The data set includes 16 variables and the training set includes 2,276 records.

Load the data and understand the data by using some stats and plots.

mtd <- read.csv("https://raw.githubusercontent.com/Rajwantmishra/DATA621_CR4/master/HW1/Deb/moneyball-training-data.csv")
med <- read.csv("https://raw.githubusercontent.com/Rajwantmishra/DATA621_CR4/master/HW1/Deb/moneyball-evaluation-data.csv")

View rows and columns, variable types

Glimpse of the data

glimpse(mtd)

## Observations: 2,276
## Variables: 17
## $ INDEX            <int> 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 15, 16, 17, 18...
## $ TARGET_WINS      <int> 39, 70, 86, 70, 82, 75, 80, 85, 86, 76, 78, 68, 72...
## $ TEAM_BATTING_H   <int> 1445, 1339, 1377, 1387, 1297, 1279, 1244, 1273, 13...
## $ TEAM_BATTING_2B  <int> 194, 219, 232, 209, 186, 200, 179, 171, 197, 213, ...
## $ TEAM_BATTING_3B  <int> 39, 22, 35, 38, 27, 36, 54, 37, 40, 18, 27, 31, 41...
## $ TEAM_BATTING_HR  <int> 13, 190, 137, 96, 102, 92, 122, 115, 114, 96, 82, ...
## $ TEAM_BATTING_BB  <int> 143, 685, 602, 451, 472, 443, 525, 456, 447, 441, ...
## $ TEAM_BATTING_SO  <int> 842, 1075, 917, 922, 920, 973, 1062, 1027, 922, 82...
## $ TEAM_BASERUN_SB  <int> NA, 37, 46, 43, 49, 107, 80, 40, 69, 72, 60, 119, ...
## $ TEAM_BASERUN_CS  <int> NA, 28, 27, 30, 39, 59, 54, 36, 27, 34, 39, 79, 10...
## $ TEAM_BATTING_HBP <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA...
## $ TEAM_PITCHING_H  <int> 9364, 1347, 1377, 1396, 1297, 1279, 1244, 1281, 13...
## $ TEAM_PITCHING_HR <int> 84, 191, 137, 97, 102, 92, 122, 116, 114, 96, 86, ...
## $ TEAM_PITCHING_BB <int> 927, 689, 602, 454, 472, 443, 525, 459, 447, 441, ...
## $ TEAM_PITCHING_SO <int> 5456, 1082, 917, 928, 920, 973, 1062, 1033, 922, 8...
## $ TEAM_FIELDING_E  <int> 1011, 193, 175, 164, 138, 123, 136, 112, 127, 131,...
## $ TEAM_FIELDING_DP <int> NA, 155, 153, 156, 168, 149, 186, 136, 169, 159, 1...

Sample 6 rows with sample 7 columns

head(mtd)

Show entire dataset

DT::datatable(mtd, options = list(pagelength=5))

#DT::datatable(med, options = list(pagelength=5))

Structure of data

paste("Dimension of dataset", dim(mtd))

## [1] "Dimension of dataset 2276" "Dimension of dataset 17"

paste("Count of dataset", count(mtd))

## [1] "Count of dataset 2276"

summary(mtd)

##      INDEX         TARGET_WINS     TEAM_BATTING_H TEAM_BATTING_2B
##  Min.   :   1.0   Min.   :  0.00   Min.   : 891   Min.   : 69.0  
##  1st Qu.: 630.8   1st Qu.: 71.00   1st Qu.:1383   1st Qu.:208.0  
##  Median :1270.5   Median : 82.00   Median :1454   Median :238.0  
##  Mean   :1268.5   Mean   : 80.79   Mean   :1469   Mean   :241.2  
##  3rd Qu.:1915.5   3rd Qu.: 92.00   3rd Qu.:1537   3rd Qu.:273.0  
##  Max.   :2535.0   Max.   :146.00   Max.   :2554   Max.   :458.0  
##                                                                  
##  TEAM_BATTING_3B  TEAM_BATTING_HR  TEAM_BATTING_BB TEAM_BATTING_SO 
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.0   Min.   :   0.0  
##  1st Qu.: 34.00   1st Qu.: 42.00   1st Qu.:451.0   1st Qu.: 548.0  
##  Median : 47.00   Median :102.00   Median :512.0   Median : 750.0  
##  Mean   : 55.25   Mean   : 99.61   Mean   :501.6   Mean   : 735.6  
##  3rd Qu.: 72.00   3rd Qu.:147.00   3rd Qu.:580.0   3rd Qu.: 930.0  
##  Max.   :223.00   Max.   :264.00   Max.   :878.0   Max.   :1399.0  
##                                                    NA's   :102     
##  TEAM_BASERUN_SB TEAM_BASERUN_CS TEAM_BATTING_HBP TEAM_PITCHING_H
##  Min.   :  0.0   Min.   :  0.0   Min.   :29.00    Min.   : 1137  
##  1st Qu.: 66.0   1st Qu.: 38.0   1st Qu.:50.50    1st Qu.: 1419  
##  Median :101.0   Median : 49.0   Median :58.00    Median : 1518  
##  Mean   :124.8   Mean   : 52.8   Mean   :59.36    Mean   : 1779  
##  3rd Qu.:156.0   3rd Qu.: 62.0   3rd Qu.:67.00    3rd Qu.: 1682  
##  Max.   :697.0   Max.   :201.0   Max.   :95.00    Max.   :30132  
##  NA's   :131     NA's   :772     NA's   :2085                    
##  TEAM_PITCHING_HR TEAM_PITCHING_BB TEAM_PITCHING_SO  TEAM_FIELDING_E 
##  Min.   :  0.0    Min.   :   0.0   Min.   :    0.0   Min.   :  65.0  
##  1st Qu.: 50.0    1st Qu.: 476.0   1st Qu.:  615.0   1st Qu.: 127.0  
##  Median :107.0    Median : 536.5   Median :  813.5   Median : 159.0  
##  Mean   :105.7    Mean   : 553.0   Mean   :  817.7   Mean   : 246.5  
##  3rd Qu.:150.0    3rd Qu.: 611.0   3rd Qu.:  968.0   3rd Qu.: 249.2  
##  Max.   :343.0    Max.   :3645.0   Max.   :19278.0   Max.   :1898.0  
##                                    NA's   :102                       
##  TEAM_FIELDING_DP
##  Min.   : 52.0   
##  1st Qu.:131.0   
##  Median :149.0   
##  Mean   :146.4   
##  3rd Qu.:164.0   
##  Max.   :228.0   
##  NA's   :286

describe(mtd)

## mtd 
## 
##  17  Variables      2276  Observations
## --------------------------------------------------------------------------------
## INDEX 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0     2276        1     1268    850.4    125.8    252.5 
##      .25      .50      .75      .90      .95 
##    630.8   1270.5   1915.5   2287.5   2407.2 
## 
## lowest :    1    2    3    4    5, highest: 2531 2532 2533 2534 2535
## --------------------------------------------------------------------------------
## TARGET_WINS 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      108        1    80.79    17.47     54.0     61.0 
##      .25      .50      .75      .90      .95 
##     71.0     82.0     92.0     99.5    104.0 
## 
## lowest :   0  12  14  17  21, highest: 128 129 134 135 146
## --------------------------------------------------------------------------------
## TEAM_BATTING_H 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      569        1     1469    149.8     1282     1315 
##      .25      .50      .75      .90      .95 
##     1383     1454     1537     1636     1695 
## 
## lowest :  891  992 1009 1116 1122, highest: 2333 2343 2372 2496 2554
## --------------------------------------------------------------------------------
## TEAM_BATTING_2B 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      240        1    241.2    52.89      167      182 
##      .25      .50      .75      .90      .95 
##      208      238      273      303      320 
## 
## lowest :  69 112 113 118 123, highest: 382 392 393 403 458
## --------------------------------------------------------------------------------
## TEAM_BATTING_3B 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      144        1    55.25    30.34       23       27 
##      .25      .50      .75      .90      .95 
##       34       47       72       96      108 
## 
## lowest :   0   8   9  11  12, highest: 166 190 197 200 223
## --------------------------------------------------------------------------------
## TEAM_BATTING_HR 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      243        1    99.61    69.49     14.0     20.0 
##      .25      .50      .75      .90      .95 
##     42.0    102.0    147.0    179.5    199.0 
## 
## lowest :   0   3   4   5   6, highest: 247 249 257 260 264
## --------------------------------------------------------------------------------
## TEAM_BATTING_BB 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      533        1    501.6    130.1    248.2    363.5 
##      .25      .50      .75      .90      .95 
##    451.0    512.0    580.0    635.0    670.2 
## 
## lowest :   0  12  29  34  45, highest: 815 819 824 860 878
## --------------------------------------------------------------------------------
## TEAM_BATTING_SO 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2174      102      822        1    735.6    282.2      359      421 
##      .25      .50      .75      .90      .95 
##      548      750      930     1049     1103 
## 
## lowest :    0   66   67   72   74, highest: 1303 1320 1326 1335 1399
## --------------------------------------------------------------------------------
## TEAM_BASERUN_SB 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2145      131      348        1    124.8    87.96     35.0     44.0 
##      .25      .50      .75      .90      .95 
##     66.0    101.0    156.0    231.0    301.8 
## 
## lowest :   0  14  18  19  20, highest: 562 567 632 654 697
## --------------------------------------------------------------------------------
## TEAM_BASERUN_CS 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1504      772      128        1     52.8    23.24       24       30 
##      .25      .50      .75      .90      .95 
##       38       49       62       77       91 
## 
## lowest :   0   7  11  12  14, highest: 171 186 193 200 201
## --------------------------------------------------------------------------------
## TEAM_BATTING_HBP 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##      191     2085       55    0.999    59.36    14.61     40.0     44.0 
##      .25      .50      .75      .90      .95 
##     50.5     58.0     67.0     76.0     82.5 
## 
## lowest : 29 30 35 38 39, highest: 87 88 89 90 95
## --------------------------------------------------------------------------------
## TEAM_PITCHING_H 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      843        1     1779    628.1     1316     1356 
##      .25      .50      .75      .90      .95 
##     1419     1518     1682     2058     2563 
## 
## lowest :  1137  1168  1184  1187  1202, highest: 16038 16871 20088 24057 30132
## --------------------------------------------------------------------------------
## TEAM_PITCHING_HR 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      256        1    105.7    70.02     18.0     25.0 
##      .25      .50      .75      .90      .95 
##     50.0    107.0    150.0    187.0    209.2 
## 
## lowest :   0   3   4   5   6, highest: 291 297 301 320 343
## --------------------------------------------------------------------------------
## TEAM_PITCHING_BB 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      535        1      553    140.7    377.0    417.5 
##      .25      .50      .75      .90      .95 
##    476.0    536.5    611.0    693.5    757.0 
## 
## lowest :    0  119  124  131  140, highest: 2169 2396 2840 2876 3645
## --------------------------------------------------------------------------------
## TEAM_PITCHING_SO 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2174      102      823        1    817.7    316.9    421.3    490.0 
##      .25      .50      .75      .90      .95 
##    615.0    813.5    968.0   1095.0   1173.0 
## 
## lowest :     0   181   205   208   252, highest:  3450  4224  5456 12758 19278
##                                                                             
## Value          0   200   400   600   800  1000  1200  1400  1600  1800  2200
## Frequency     20     7   211   554   593   580   156    35     7     2     1
## Proportion 0.009 0.003 0.097 0.255 0.273 0.267 0.072 0.016 0.003 0.001 0.000
##                                               
## Value       2400  3400  4200  5400 12800 19200
## Frequency      3     1     1     1     1     1
## Proportion 0.001 0.000 0.000 0.000 0.000 0.000
## 
## For the frequency table, variable is rounded to the nearest 200
## --------------------------------------------------------------------------------
## TEAM_FIELDING_E 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     2276        0      549        1    246.5    190.4    100.0    109.0 
##      .25      .50      .75      .90      .95 
##    127.0    159.0    249.2    542.0    716.0 
## 
## lowest :   65   66   68   72   74, highest: 1567 1728 1740 1890 1898
## --------------------------------------------------------------------------------
## TEAM_FIELDING_DP 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1990      286      144        1    146.4    29.29       98      109 
##      .25      .50      .75      .90      .95 
##      131      149      164      178      186 
## 
## lowest :  52  64  68  71  72, highest: 215 218 219 225 228
## --------------------------------------------------------------------------------

names(mtd)

##  [1] "INDEX"            "TARGET_WINS"      "TEAM_BATTING_H"   "TEAM_BATTING_2B" 
##  [5] "TEAM_BATTING_3B"  "TEAM_BATTING_HR"  "TEAM_BATTING_BB"  "TEAM_BATTING_SO" 
##  [9] "TEAM_BASERUN_SB"  "TEAM_BASERUN_CS"  "TEAM_BATTING_HBP" "TEAM_PITCHING_H" 
## [13] "TEAM_PITCHING_HR" "TEAM_PITCHING_BB" "TEAM_PITCHING_SO" "TEAM_FIELDING_E" 
## [17] "TEAM_FIELDING_DP"

str(mtd)

## 'data.frame':    2276 obs. of  17 variables:
##  $ INDEX           : int  1 2 3 4 5 6 7 8 11 12 ...
##  $ TARGET_WINS     : int  39 70 86 70 82 75 80 85 86 76 ...
##  $ TEAM_BATTING_H  : int  1445 1339 1377 1387 1297 1279 1244 1273 1391 1271 ...
##  $ TEAM_BATTING_2B : int  194 219 232 209 186 200 179 171 197 213 ...
##  $ TEAM_BATTING_3B : int  39 22 35 38 27 36 54 37 40 18 ...
##  $ TEAM_BATTING_HR : int  13 190 137 96 102 92 122 115 114 96 ...
##  $ TEAM_BATTING_BB : int  143 685 602 451 472 443 525 456 447 441 ...
##  $ TEAM_BATTING_SO : int  842 1075 917 922 920 973 1062 1027 922 827 ...
##  $ TEAM_BASERUN_SB : int  NA 37 46 43 49 107 80 40 69 72 ...
##  $ TEAM_BASERUN_CS : int  NA 28 27 30 39 59 54 36 27 34 ...
##  $ TEAM_BATTING_HBP: int  NA NA NA NA NA NA NA NA NA NA ...
##  $ TEAM_PITCHING_H : int  9364 1347 1377 1396 1297 1279 1244 1281 1391 1271 ...
##  $ TEAM_PITCHING_HR: int  84 191 137 97 102 92 122 116 114 96 ...
##  $ TEAM_PITCHING_BB: int  927 689 602 454 472 443 525 459 447 441 ...
##  $ TEAM_PITCHING_SO: int  5456 1082 917 928 920 973 1062 1033 922 827 ...
##  $ TEAM_FIELDING_E : int  1011 193 175 164 138 123 136 112 127 131 ...
##  $ TEAM_FIELDING_DP: int  NA 155 153 156 168 149 186 136 169 159 ...

mtd %>%
  summary() %>%
  kable() %>%
  kable_styling()

train <- mtd
test <- med
train$INDEX <- NULL
test$INDEX <- NULL

cleanNames <- function(train) {
    name_list <- names(train)
    name_list <- gsub("TEAM_", "", name_list)
    names(train) <- name_list
    train
}

mtd <- cleanNames(train)
med <- cleanNames(test)

Visualize the data

mtd %>%
  gather(variable, value, TARGET_WINS:FIELDING_DP) %>%
  ggplot(., aes(value)) + 
  geom_density(fill = "indianred4", color="indianred4") + 
  facet_wrap(~variable, scales ="free", ncol = 4) +
  labs(x = element_blank(), y = element_blank())

In the histogram plot above, we see that the batting, pitching home-run and batting strike-out variables are bi modal. TARGET_WINS and TEAM_BATTING_2B has most the normal distribution. PITCHING_H and PITCHING_SO have the most skewed data distribution. The skewed graphs are all rght-skewed except BATTING_BB.

scatterplot3d(mtd$TARGET_WINS, mtd$BATTING_2B, mtd$BATTING_BB, pch = 20, highlight.3d = TRUE, type = "h", main = "3D ScatterPlots")

The above 3-D scatter plot, shows the data variance between the TARGET_WINS, TEAM_BATTING_2B and TEAM_BATTING_BB to provide a comparative view.

par(mfrow=c(3,2))   
for (i in 1:16) {
      hist(mtd[,i],main=names(mtd[i]),xlab=names(mtd[i]),breaks = 51)
      boxplot(mtd[,i], main=names(mtd[i]), type="l",horizontal = TRUE)
      
      plot(mtd[,i], mtd$TARGET_WINS, main = names(mtd[i]), xlab=names(mtd[i]))
      abline(lm(mtd$TARGET_WINS ~ mtd[,i], data = mtd), col = "blue")
}

As can be seen from above histogram, boxplot and scatter plot with regression line shows the spread of the data points. More than half of the variables show skewness. A box-cox transformation may help to mitigate the skewness.

Missing or NA Values

We are trying to see how many NA is present in the dataset.

mtd %>% 
  gather(variable, value) %>%
  filter(is.na(value)) %>%
  group_by(variable) %>%
  tally() %>%
  mutate(percent = n / nrow(mtd) * 100) %>%
  mutate(percent = paste0(round(percent, ifelse(percent < 10, 1, 0)), "%")) %>%
  arrange(desc(n)) %>%
#  rename(`Variable Missing Data`=variable,`Number of Records`=n,`Share of Total`=percent) %>%
  kable() %>%
  kable_styling()

The variable BATTING_HBP (hit by pitcher) is missing over 90% of it’s data.

Zero Values

mtd %>% 
  gather(variable, value) %>%
  filter(value == 0) %>%
  group_by(variable) %>%
  tally() %>%
  mutate(percent = n / nrow(mtd) * 100) %>%
  mutate(percent = paste0(round(percent, ifelse(percent < 10, 1, 0)), "%")) %>%
  arrange(desc(n)) %>%
#  rename("Variable With Zeros"=variable,"Number of Records"=n,"Share of Total"=percent) %>%
  kable() %>%
  kable_styling()

As can be inferred from above, there are Very few zero values exists.

Checking for outliers

ggplot(stack(mtd), aes(x = ind, y = values)) +
  geom_boxplot() +
  coord_cartesian(ylim = c(0, 2500)) +
  theme(legend.position="none") +
  theme(axis.text.x=element_text(angle=45, hjust=1)) +
  theme(panel.background = element_rect(fill = 'grey'))

The box plots reveal that a great majority of the explanatory variables have high variances. Many of the medians and means are also not aligned which demonstrates the outliers’ effects.

The variance of some of the explanatory variables greatly exceeds the variance of the response “win” variable. The dataset has many outlines with some observations that are more extreme than the 1.5 * IQR of the box plot whiskers.

Checking for skewness in the data

melt(mtd) %>%
  ggplot(aes(x= value)) +
    geom_density(fill='red') + facet_wrap(~variable, scales = 'free')

As per above, there are several variables like PITCHING_H, PITCHING_BB, PITCHING_SO and FIELDING_E are extremely skewed as there are many outliers.

Finding correlations: Below shows the comparative correlations between the 16 variables as it shows the correlation coefficients and thus find correlated variables. Whichever adhere to a fitted straight red line well, ie. change in synch with each other. If the points lie close to the line but the line is curved, it’s good nonlinear association and one can still be defined by other. Each individual plot shows the relationship between the variable in the horizontal vs the vertical of the grid. Each individual plot shows the relationship between the variable in the horizontal vs the vertical of the grid, whereas the diagonal is showing a histogram of each variable.

DT::datatable(cor(drop_na(mtd[,])), options = list(pagelength=5))

pairs.panels((mtd[,])[1:8])

As can be seen from above, TARGET_WINS vs BATTING_2B is continuous and hence correlated and so is BATTING_BB and BATTING_HR.

pairs.panels((mtd[,])[9:16])

As can be seen from above, BASERUN_CS vs BATTING_HBP is continuous and hence correlated whereas PITCHING_SO and FIELDING_E is not correlated at all.

cor_res <- cor(mtd, use = "complete.obs")
mtd %>% 
  cor(., use = "complete.obs") %>%
  corrplot(., method = "color", type = "upper", tl.col = "black", diag = FALSE)

Also, there are some negatively correlated variables. According to the correlation heatmap, the values that correspond most positively are BATTING_H, BATTING_2B, BATTING_HR, BATTING_BB, PITCHING_H, PITCHING_HR, and PITCHING_BB.

mtd %>%
  gather(variable, value, -TARGET_WINS) %>%
  ggplot(., aes(value, TARGET_WINS)) + 
  geom_point(fill = "indianred4", color="indianred4") + 
  geom_smooth(method = "lm", se = FALSE, color = "black") + 
  facet_wrap(~variable, scales ="free", ncol = 4) +
  labs(x = element_blank(), y = "Wins")

Above shows how the data is distributed when compared to the linear regression. Clearly, PITCHING_H and PITCHING_SO are highly heteroscedastic. Comparatively, BATTING_HBP is most homoscedastic.

cor_res[,1:2]

##             TARGET_WINS   BATTING_H
## TARGET_WINS  1.00000000  0.46994665
## BATTING_H    0.46994665  1.00000000
## BATTING_2B   0.31298400  0.56177286
## BATTING_3B  -0.12434586  0.21391883
## BATTING_HR   0.42241683  0.39627593
## BATTING_BB   0.46868793  0.19735234
## BATTING_SO  -0.22889273 -0.34174328
## BASERUN_SB   0.01483639  0.07167495
## BASERUN_CS  -0.17875598 -0.09377545
## BATTING_HBP  0.07350424 -0.02911218
## PITCHING_H   0.47123431  0.99919269
## PITCHING_HR  0.42246683  0.39495630
## PITCHING_BB  0.46839882  0.19529071
## PITCHING_SO -0.22936481 -0.34445001
## FIELDING_E  -0.38668800 -0.25381638
## FIELDING_DP -0.19586601  0.01776946

Above shows the correlation coefficient of each variable compared to TARGET_WINS and BATTING_H.

Histogram of Variables

hist.data.frame(mtd)

par(mfrow=c(2,3))
plot(TARGET_WINS ~ BATTING_H,mtd)
  abline(lm(TARGET_WINS ~ BATTING_H,data = mtd),col="blue")
plot(TARGET_WINS ~ BATTING_2B,mtd)
  abline(lm(TARGET_WINS ~ BATTING_2B,data = mtd),col="blue")
plot(TARGET_WINS ~ BATTING_3B,mtd)
  abline(lm(TARGET_WINS ~ BATTING_3B,data = mtd),col="blue")
plot(TARGET_WINS ~ BATTING_HR,mtd)
  abline(lm(TARGET_WINS ~ BATTING_HR,data = mtd),col="blue")
plot(TARGET_WINS ~ BATTING_BB,mtd)
  abline(lm(TARGET_WINS ~ BATTING_BB,data = mtd),col="blue")
plot(TARGET_WINS ~ BATTING_SO,mtd)
  abline(lm(TARGET_WINS ~ BATTING_SO,data = mtd),col="blue")

plot(TARGET_WINS ~ BASERUN_SB,mtd)
  abline(lm(TARGET_WINS ~ BASERUN_SB,data = mtd),col="blue")
plot(TARGET_WINS ~ BASERUN_CS,mtd)
  abline(lm(TARGET_WINS ~ BASERUN_CS,data = mtd),col="blue")
plot(TARGET_WINS ~ PITCHING_H,mtd)
  abline(lm(TARGET_WINS ~ PITCHING_H,data = mtd),col="blue")
plot(TARGET_WINS ~ PITCHING_HR,mtd)
  abline(lm(TARGET_WINS ~ PITCHING_HR,data = mtd),col="blue")
plot(TARGET_WINS ~ PITCHING_BB,mtd)
  abline(lm(TARGET_WINS ~ PITCHING_BB,data = mtd),col="blue")
plot(TARGET_WINS ~ PITCHING_SO,mtd)
  abline(lm(TARGET_WINS ~ PITCHING_SO,data = mtd),col="blue")

plot(TARGET_WINS ~ FIELDING_E,mtd)
  abline(lm(TARGET_WINS ~ FIELDING_E,data = mtd),col="blue")
plot(TARGET_WINS ~ FIELDING_DP,mtd)
  abline(lm(TARGET_WINS ~ FIELDING_DP,data = mtd),col="blue")

This shows very few variables are normally distributed.

vis_miss(mtd)